Nowcasting the current size of the COVID-19 outbreak in the United States

Algorithm

We wish to estimate (nowcast) the total current size of the COVID-19 outbreak, i.e. the total number of non-isolated individuals currently infected with SARS-CoV2. We need to estimate this number from case reports (the number of newly confirmed cases on a given day).

Case reports do not reflect those who are symptomatic but not yet diagnosed, nor those with latent infections (those who cary the virus but are not yet symptomatic). In addition, a number of individuals may be infected but never develop sysmptoms. These asymptomatic individuals may still transmit the virus. We assume that cases are isolated from the community at the time the case is reported.

In order to estimate the outbreak size, we must first estimate the number of symptomatic and latent infections in the community, accounting for cases that would be missed because they would never show symptoms, then sum those.

Algorithm details:

From case reports (the number of newly confirmed cases), we use monte carlo simulation to construct a line list, i.e. a list of symptom onset times for each individual case. The average delay from symtpom onset to case notification for the US is 2.67 days¹. Individual simulated symtom onset times are distributed randomly around 2.67 days before the reporting date (exponential distribution).

A second simulation produces exposure dates for each infected individual. The average incubation period for the US is 7.67 days². Individual simulated exposure times are distributed randomly around 7.67 days before the symptom onset date (gamma distribution with shape parameter ~4.18).

Now we have a complete line list for each case, including exposure date, symptom onset date, and reporting date (which is also the isolation date).

From the line list, we sum the number of individuals with latent infections on each date to produce a curve of the numbr of latent cases in the community. We do the same to find the number of individuals symptomatic infections on each date. These curves represent only the Latent and Symptomatic cases that were eventually reported.

Based on testing of passengers on the Princes Cruises ship in Yokohama, Japan, Mizumoto et al. estimated that the proportion of cases that are asymptomatic is 34.6% (95% CrI: 29.4%–39.8%)³. We assume asymptomatic cases are never detected. To account for these, we multiply both the number of Symptomatic cases and the number of Latent cases by \(\frac{1}{34.6\%}\).

Since the symptom onsets occur on average 2.67 days before reporting, we are only sure to have a complete estimate for the number of symptomatic individuals at some time prior to 2.67 days befor the present. We therefore throughout our estimates for the last several days, and forecast the number of Symptomatic individuals from that day back to the present. This is the “nowcast” of symptomatic individuals. We do the same for the curve of Latent individuals, throwing out estimates much prior to 7.67 before our last trusted estimate for the number of symtpomatic. Forecasting the number of Latent from that point forward gives us a nowcast of latent infections.

The sum of the Latent and Symptomatic curves and/or their forecasted curves gives us the estimate of the total number of infected, into the present.

Data

US Case Reports by State

US data are maintained by CEID and available here.

Data are compiled from https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_the_United_States, which is updated by anonymous contributors.

We aim to update our dataset daily.